An Elasticity Approach to the Solidification of Fibre-Reinforced Shells

This paper presents a model of solidification for a fibre-reinforced circular cylindrical channel section under plane strain. Cooling from the inside surface of a cylindrical section of the liquid phase causes a solidification front to move radially through the thickness until solidification is complete. The principal area of interest is the mechanism by which the nature of the temperature field during solidification affects the shape and residual stresses in the final solid part. A special case of the solution is presented and compared with an equivalent result in which solidification of the whole section occurs instantaneously. The mechanism is also relevant to microstructural wrinkling. This revised version was published online in August 2006 with corrections to the Cover Date.     

Residual stresses in gas-assisted injection molding

Residual stresses are a major issue in the mechanical and optical behavior of injection-molded parts. In this study, we analyze their development in the case of gas-assisted injection molding (GAIM) of amorphous polymers. Flow-induced residual stresses are computed within a decoupled approach, in which elastic effects are neglected in the momentum balance, assuming a generalized Newtonian material behavior. In a staggered procedure, the computed viscous flow kinematics are used to calculate normal stresses employing a compressible version of the Rolie-Poly model. For the computation of thermally and pressure-induced residual stresses, a linear thermo-viscoelastic model is used. A 3-D finite element model for GAIM is employed, which is able to capture the kinematics of the flow front and whose capabilities to predict the thickness of the residual material layer have been validated by Haagh and Van de Vosse (Int J Numer Methods Fluids 28:1355–1369, 1998). In order to establish a clear comparison, the development of residual stresses is analyzed using standard injection molding and GAIM for a test geometry.     

A Dynamic Method for the Residual Stress Measurement During Polymer Crystallization

A new dynamic method based on bilayer system is proposed to characterize the residual stress formation during the crystallization of semi-crystalline polyethylene glycol 10000 (PEG10000). The resin is coated on a solid polymeric film to create a filmsubstrate compound. Its temperature field and dynamic deflection are monitored by synchronized optical and thermography cameras. The crystallization kinetics is first characterized from the former information. Then a simple dynamic model is proposed to relate the dynamic deflection with crystallization process. Residual stresses are established and in the range of 0–2.1 MPa. The generation of residual stresses is due to the edge constraints of the cantilever beam and to the increase of viscosity during solidification that allows the polymer to carry tensile loadings. The spherulite impingement is found to be important for this period from a microscopic view. Boundary condition should be well controlled to steer residual stresses. Such method is promising to measure residual stresses at the micro-scale for polymers to be spread on a flexible substrate and can mimic different mechanical situations of interest.     

Measurement of the Distribution of Residual Stresses in Layered Thick-Walled GFRP Pipes

The objective of this study is to measure the axial, circumferential, shear and radial residual stress distributions in three thick-walled glass fibre reinforced plastic (GFRP) filament-wound pipes, two of which are layered. The measurement of residual stresses was carried out using a recently published layer removal method which overcomes the limitations of previous techniques and can be applied to layered anisotropic pipes of any wall thickness. Layers of approximately 0.3 mm thickness were incrementally ground from the outer surface of the pipes. The resulting strains were measured on the inner surfaces. A least-squares polynomial was fitted to each measured data set, and used to calculate the corresponding stress distributions. All of the resulting axial, hoop and shear stress distributions adhere to the requirement of self-equilibrium and the radial stress distributions all vanish to zero at the inner and outer surfaces. The radial stresses of the layered pipes showed a tendency to have two peaks, one for each layer, a consequence of the two-stage manufacturing process of these pipes. The measured axial and hoop stresses of all three pipes were similar at the inner surfaces despite significant differences in the stiffnesses in the principal directions arising from different wind angles.     

An assessment of residual-stress measurements around cold-worked holes

An X-ray diffraction technique was employed to determine the residual stresses introduced by cold working a fastener hole in a 6-mm thick 2024-T351 aluminum plate. The radial and tangenital residual stresses were measured at both faces of the plate and the measurements compared with the results from a two-dimensional axisymmetric finite-element model. The comparisons were favorable, although modifying the finite-element model to simulate the X-ray process provided better agreement. Experimental determinations of residual stresses showed differences between the two faces of the plate. This feature was attributed to the directional nature of the cold-working process. Paper was presented at the 1994 SEM Spring Conference on Experimental Mechanics held in Baltimore, MD on June 8–10.     

Determination of crack spacing and penetration due to shrinkage of a solidifying layer

A method based on energy minimisation is used to determine the spacing and penetration of a regular array of cracks in a layer of material whose thickness is increasing as it solidifies from a liquid. After solidification, the slab shrinks and subsequently cracks due to internal stresses. A simple Stefan solidification model is used to determine the thickness of the slab as time progresses as well as the temperature profile in the slab. The key feature of the results is that a minimum crack spacing occurs early in the solidification process and this minimum defines a basic spacing for the crack array. The minimum spacing occurs for a range of constraints (boundary conditions) and thermal profiles in the material, indicating the robustness of the phenomenon. Cracks propagating with the unique minimum spacing are subject to a period doubling instability that acts to coarsen the crack pattern, which brings the crack spacing close to the minimum energy state for later time. Good numerical comparison between the crack spacings predicted by energy minimisation and those observed in basalt columns is demonstrated.     

Stress state in glass bodies degassed under heating by infrared radiation

A model is proposed to calculate stresses in a glass layer with gas impurities heated by thermal infrared radiation. Calculations were performed for a layer with a diatomic impurity of nitric oxide and a triatomic impurity of water. It is shown that for the radiation parameters and impurity concentrations considered, the presence of nitric oxide in the layer does not influence its stress state, whereas the presence of water leads to a certain increase of stress. The stress state of the layer is determined by the level of thermal stresses, and theconcentration stresses and the stresses due to the mass forces of radiation are negligible. An increase in the rate of diffusion of the diatomic impurity due to a change of the radiation spectrum is accompanied by an increase of thermal stresses.     

A numerical and experimental investigation into residual stress in thermally sprayed coatings

This paper is concerned with an investigation into the thermal spray process and is particularly concerned with the residual stresses that arise when a steel-alloy coating is sprayed onto a copper-alloy substrate. This material combination was used recently to enhance the thermal and mechanical efficiency of the pressure die casting process. A difficulty with the spraying of steel on copper is the attainment of appreciable thickness of the coating due to debonding during the thermal spraying process. Prominent among possible causes of debonding is residual stress, which is the focus of the research presented in the paper. An investigation into the thermal spray process is performed using experimentation, simplified numerical modelling and finite element modelling. The development of residual stress for a range of process parameters, i.e. deposited layer thickness, interval of layer deposition and the number of layers in a coating (i.e. block deposition versus multilayer deposition for a desired coating thickness) is recorded. The results from the three investigation methods agreeably indicate a progressive change in average interfacial residual stress from compressive towards tensile with increase in thickness of deposited layer; and a tensile interfacial stress in a two-layer coating, which increases with increase in interval of deposition between the two layers. On the whole, the observations from the results suggest an increase in potential for coating debonding with increase in both deposited layer thickness and layer deposition interval. The results further suggest higher potential for coating debonding with block deposition compared to multilayer deposition for a desired coating thickness.     

Prediction of nonlinear viscoelastic behavior of polymeric composites using an artificial neural network

Creep tests at constant stress are performed for the carbon-fiber reinforced epoxy composite at various temperatures and initial stresses. A nonlinear viscoelastic constitutive model is developed, and its material parameters are determined by fitting it to creep test data. Model results are found to agree very well with the experimental data at low temperature and low stress conditions. However, the agreement deteriorates at high temperatures, particularly in the vicinity of the glass transition temperature.An alternative model based on an artificial neural network (ANN) is developed to predict the stress relaxation of the polymer matrix composite. The ANN model is trained and validated with 9000 experimental data sets obtained from stress relaxation tests performed at various constant strain (initial stress) and constant temperature conditions. Training of the ANN employs a scaled conjugate gradient method. The optimal brain surgeon algorithm is employed to optimize the topology. The optimal ANN configuration has 88 processing elements (3 in the input layer, 45 in the first hidden layer, 39 in the second hidden layer, and 1 in the output layer) and 410 links. The predictions of the ANN model are found to be more accurate over a wider range of stress and temperature conditions than those of the explicit nonlinear viscoelastic model, in particular near the glass transition temperature.     

Method of calculating residual stresses in semicircular notches in a surface hardened hollow cylindrical specimen

A method is proposed to study the distribution of residual stresses in a semicircular notch in a hollow cylindrical specimen after advanced surface plastic deformation. The initial information used in the method is one or two experimentally determined components of the residual stress tensor in the hardened layer of the smooth specimen. The problem is solved using a finite element technique taking into account initial plastic strains, which are set in correspondence to the residual stresses according to the laws of elasticity. The effect of the hardening technology and notch depth on the distribution of residual stresses is studied. Experimental verification of the method showed that the calculated and experimental data on the stress distribution over the depth of the layer are in good agreement.     

Calculation of residual stresses in injection molded products

Both flow- and thermally-induced residual stresses which arise during the injection molding of amorphous thermoplastic polymers are calculated in the filling and post-filling stage. To achieve this, a compressible version of the Leonov model is employed. Two techniques to calculate flow-induced residual stresses are investigated. First, a direct approach is developed where the pressure problem is formulated using the viscoelastic material model. Second, generalized Newtonian material behavior is assumed in formulating the pressure problem, and the resulting flow kinematics is used to calculate normal stresses employing the compressible Leonov model. The latter technique gives comparable results, while reducing the computational cost significantly.     

Effect of residual stresses on the crack-tip constraint in a modified boundary layer model

Residual stresses play a crucial role in structural integrity assessment. In this study, a large cracked cylinder with a weld in the center is applied to investigate the effect of residual stresses on the crack-tip constraint. A modified boundary layer model with a remote displacement-controlled elastic K-field and T-stress under small scale yielding has been used to simulate the problem. A two-dimensional tensile residual stress field due to the weld is introduced into the model by the so-called eigenstrain method. It has been shown that the residual stresses can significantly elevate the crack-tip constraint and thus increase the probability for cleavage fracture. The constraint parameter R introduced by the authors can be used to rank the crack-tip constraint induced by the bi-axial residual stresses. The R value decreases with the increase in the applied J-integral. The residual stress-induced constraint is also coupled with the T-stress. The R value becomes smaller with larger T-stress.     

On the studies of residual stresses in glass plates

The theoretical foundation of the photoelastic methods being presently used for measuring and analyzing residual stresses in glass is insufficient for studying development of transient viscoelastic stress states in glass plates during tempering process and for an explanation of the actual material behavior. It is shown that the basic knowledge of photoviscoelastic effect in glass over a wide range of electromagnetic radiation and temperature is necessary for such on analysis. Some photoelastic properties of plate glass are presented.     

A receding contact problem for an anisotropic elastic medium consisting of a layer and a half plane

This paper considers a frictionless receding contact problem between an anisotropic elastic layer and an anisotropic elastic half plane, when the two bodies are pressed together by means of a rigid circular stamp. The problem is reduced to a system of singular integral equations in which the contact stresses and lengths are the unknown functions. Numerical results for the contact stresses and the contact lengths are given by depending on various fibre orientations.     

Molten droplet solidification and substrate remelting in microcasting Part I: numerical modeling and experimental verification

This paper presents a numerical model of a molten metal droplet impinging, solidifying and bonding to a solid substrate. The physical and numerical model includes dissimilar materials, multi-dimensional axisymmetric heat transfer, tracking of solid/liquid interfaces during remelting and solidification, and coupled treatment of the continuous droplet/substrate region. The numerical model solves for the evolution of the temperature distribution in the droplet and substrate, predicts the position of the remelting and solidification fronts, and accounts for convective motion. The effect of the convection induced by the droplet spreading is modeled through a time-dependent effective thermal conductivity. High-speed filming of the molten droplet impinging and spreading on the substrate is performed to obtain the required parameters to determine this time dependent effective conductivity. The accuracy of the model is investigated with experimental techniques. This research is directly related to the development of microcasting Shape Deposition Manufacturing (SDM) which is a process for automatically fabricating complex multi-material objects by sequentially depositing material layers. Microcasting is a molten metal droplet deposition process in SDM, which is able to create fully dense metal layers with controlled microstructure. Important issues in the production of high quality objects manufactured with microcasting SDM are: attainment of interlayer metallurgical bonding through substrate remelting, control of both substrate and droplet cooling rates, and minimization of residual thermal stresses. To validate experimentally the numerical modeling approach, predicted cooling rates are compared with thermocouple measurements and substrate remelting depths are verified through optical metallographic techniques. Received on 10 June 1998     

汽轮机轮盘热处理残余应力分析

百万核电汽轮机红套低压转子工作环境的蒸汽参数较低,各级轮盘均处于湿度较大的工作区域,易产生应力腐蚀,引起裂纹萌生和扩展．为提高轮盘的抗腐蚀能力,降低工作应力是一个有效的方法．通过热处理方法,在轮盘表面形成预压应力以抵消部分旋转拉应力是可行的方法,而产生适当深度和大小的预压应力则需对热处理过程进行谨慎的设计．本文以汽轮机轮盘为研究对象,建立轴对称有限元模型,通过对ABAQUS软件的二次开发,实现对轮盘热处理过程的温度场及应力场进行数值模拟．计算综合考虑了非线性的材料热物性参数、力学性能参数、表面换热系数及不同材料组织转变的相变潜热、热物性参数和力学参数,通过对不同热处理方法得到的残余应力场的比较,获得了较合理的水冷方式,为热处理工艺确定提供参考．     

Thermal residual stresses in thick graphite/epoxy composite laminates—Uniaxial approach

Thermal residual stresses have been known to be very large in laminates of continuous-fiber-reinforced polymer composites. When the thickness of the laminate is large, however, the measurement of the residual stresses raises questions on the accuracy of the conventional methods. A novel concept of layer separation is developed to measure quantitatively and precisely the tensile residual stresses in thick plates with layered distribution of residual stresses. It is applied to thick [O₂/9O₄]_13s, AS/3501-6 graphite/epoxy laminates. The test specimens were mechanically modeled into the thin strips for the application of the new concept of layer separation. The tensile residual stresses measured in the 90-deg layers of these laminates are nonuniform throughout the specimen, and vary from 55.6 MPa to 71.4 MPa. It is very interesting to compare these values with the transverse strengthF ₂ ^tu of AS/3501-6 unidirectional composites, which is 65.4 MPa.     

Residual stresses and mechanical properties of a ZnO pyroelectric sensor

The multilayer composite film stack is a common feature of the microsensors based on thin film technology. In this paper, we propose an analytical model to investigate the Young’s moduli, hardness, and residual stresses of the constitutive film layers of a multilayer film stack. A multilayer film stresses model is derived to evaluate the residual stress distributions in the constitutive film layers of a ZnO pyroelectric sensor. A good agreement among the multilayer film stresses model, the grain morphologies characterized by scanning electron microscopy, the mechanical properties testing by nanoindentation, and the voltage responsivity measurement of the ZnO pyroelectric sensor is found in this paper. The proposed multilayer film stresses model can therefore be used to quantitatively analyze the film stresses and proceed to the optimization of thin film deposition process.     

Direct method of solving the boundary-value problem of relaxation of residual stresses in a hardened cylindrical specimen under creep conditions

A direct method of solving a boundary-value problem for a surface-hardened cylindrical specimen affected by a tensile load under creep conditions is proposed. Relations for estimating the kinetics of the stress-strain state in the hardened layer are obtained. The adequacy of the solution is verified by experimental data on relaxation of residual stresses in the hardened layer of a cylindrical specimen made of éI 691 steel at T = 400°C. The calculated and experimental residual stresses are demonstrated to be in good agreement.     

Evaluation of the residual stresses due to the sintering process of diamond–metal matrix hot-pressed tools

The sintering process of diamond–metal matrix hot-pressed tools, usually used for cutting hard materials (e.g., stone cutting) originates residual stresses, which should be taken into account in the performance of the tool. The work concerns the use of finite element simulation for modelling of thermal residual stresses generated during the sintering process of metal matrix diamond tools normally employed by the industry. Stress distribution fields were determined for two different diamond shapes (modelled with 2D axisymmetric elements, with the sphere shape generated from the revolution of one circle and the octahedron shape generated from the revolution of one octagon, respectively) using an 8-node biquadratic axisymmetric quadrilateral, reduced integration element type CAX8. The thermal residual stress field in the nearby region of a diamond particle with the shape generated from the octagon is examined by using three different matrix materials, each one sintered at different temperatures. The analyses have demonstrated how much the residual stresses are sensitive to the stress–strain behaviour of the metal matrices.